Superintegrable systems with spin in two- and three-dimensional Euclidean spaces
P. Winternitz, I. Yurdusen
TL;DR
This paper extends the concept of superintegrability in quantum mechanics to particles with spin, constructing new systems with high-dimensional Lie algebras of integrals in 2D and 3D spaces.
Contribution
It introduces novel superintegrable systems involving spin-1/2 particles interacting with spin-0 particles, expanding the class of known superintegrable models.
Findings
Constructed 8-dimensional Lie algebra systems in 2D
Developed 9-dimensional Lie algebra systems in 3D
Extended superintegrability concepts to spin interactions
Abstract
The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s=1/2 interacting with one of spin s=0. Non-trivial superintegrable systems with 8- and 9-dimensional Lie algebras of first-order integrals of motion are constructed in two- and three-dimensional spaces, respectively.
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